It is commonly known that at high(er) temperatures, resummations are in order to save the perturbative expansion, see e.g. [1]}, [2]} or the reviews [3]}, [4]}. We will not attempt this here, as our main focus was on determining the deconfinement transition and its interplay with the dimension two condensates. Our findings are however clear: the critical deconfinement estimate, \(T_c\approx 0.231\)  GeV, is very close to the one loop estimate reported in [5]} using the \(T=0\)  Curci–Ferrari mass fit parameter, namely \(T_c\approx 0.238\)  GeV. We repeat here we did not use any external (lattice) input, except for the estimate of \(\Lambda _{\overline{\mbox{\tiny {MS}}}}\)  of course. A posteriori, this is not such a surprise: the used value for the (temperature independent) gluon mass in [5]} was \(m(T)\approx 0.710\)  GeV, whilst here we find that the dynamical \(m(T)\)  indeed varies only little from its \(m(T=0)\approx 0.670\)  GeV value (cfr. (REF )), next to a pretty small asymmetry. For the record, functional approaches as in [7]} arrived at \(T_c=0.230\pm 0.023\)  GeV, i.e. all values in the same ballpark. This extends to the variational estimate of [8]}, \(T_c\approx 0.239\)  GeV, or the Coulomb gauge variational estimate \(T_c\approx 0.275-0.290\)  GeV [9]}. For comparison, lattice estimates for the SU(2) transition temperate are \(T_c\approx 0.295\)  GeV [10]} or \(T_c\approx 0.312\)  GeV [11]}, [8]}.
